would normally rely on sufficiently strong hydrodynamic connectivity expressed by the lower bound on the density \(\rho (\cdot ,t) \gtrsim \frac{1}{\sqrt{1+t}}\) ,
see [1]} and also [2]}. Such a power lower bound is not available for general non-vacuous solutions, except for the case of global singular metric kernels in 1D, or under certain threshold condition in smooth kernel case, see [3]}, [4]}, [5]}, [6]}.
